In topology optimization, the objective function is a convex combination of field strength and potential convexity. The vanishing force in the trapping center is ensured by assuming the geometry and feeding invariant with respect to the \(\sigma _z C_{4z}\)  operation [1]}, see Appendix . Optimization is applied to a spherical shell fed by four identical sources placed at the maxima of the optimal current density shown in Fig. REF . The performance of Pareto-optimal designs obtained by topology optimization is shown in Fig. REF . Furthermore, Fig. REF  shows the design corresponding to black cross mark in Fig. REF . The shape of the potential well generated by the current through this trap is included in Fig. REF .
<FIGURE>